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Polymer-stabilized blue phase liquid crystal with
a negative Kerr constant
Yan Li,1 Yuan Chen,
1 Jin Yan,
1 Yifan Liu,
1 Jianpeng Cui,
1,2 Qionghua Wang,
2 and
Shin-Tson Wu1,*
1CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, FL 32816, USA 2School of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China
*swu@mail.ucf.edu
Abstract: A polymer-stabilized blue-phase liquid crystal (BPLC) with a
negative Kerr constant is reported. In a voltage-on state, the double-twist
BPLC molecules within the lattice cylinders are reoriented perpendicular to
the applied electric field because of their negative dielectric anisotropy. As a
result, the induced birefringence has a negative value, which leads to a
negative Kerr constant. The negative sign of Kerr constant is experimentally
validated by using a quarter-wave plate and a vertical field switching cell.
Such a BPLC shows a negligible (~1%) hysteresis and fast response time
(~1ms) at the room temperature, although its Kerr constant is relatively
small because the employed host has a small ∆ε.
©2012 Optical Society of America
OCIS codes: (160.3710) Liquid crystals; (160.5470) Polymers.
References and links
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#172891 - $15.00 USD Received 18 Jul 2012; accepted 24 Jul 2012; published 26 Jul 2012(C) 2012 OSA 1 August 2012 / Vol. 2, No. 8 / OPTICAL MATERIALS EXPRESS 1135
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1. Introduction
Blue phase liquid crystal (BPLC) [1,2] is a self-assembled nano-structured composite. It is
typically comprised of 90-95wt% nematic LC host and 5-10wt% chiral dopant with a high
helical twisting power (HTP>100) [3]. Most of BPLCs studied so far employ a positive
dielectric anisotropy (∆ε) LC host. If the LC host has a positive ∆ε, then the electric-field-
induced birefringence ∆nind, which is defined as ne(E)-no(E), will also have a positive sign,
and vice versa. BPLCs with negative ∆ε LC hosts have been investigated since 1980s [4,5].
However, the temperature range of such a BPLC is too narrow to be practically useful.
Moreover, the measured induced birefringence is easily affected by the lattice distortion and
phase transition because of the soft BPLC structure. This is evidenced by the relatively slow
response time, a few milliseconds instead of submillisecond, as reported in [2].
Another approach for obtaining negative induced birefringence (or negative Kerr constant)
is to utilize Debye relaxation of a positive ∆ε LC host [6]. As frequency increases, the bulky
LC molecules can no longer follow the electric field so that the initially positive Kerr constant
gradually decreases and eventually turns to negative. Recently, an interesting approach to
obtain a negative Kerr constant with a dual frequency liquid crystal (DFLC) is demonstrated
[7]. Such a BPLC exhibits an attractive feature: by switching the frequency of the applied
electric field, both positive and negative Kerr constants can be realized, which results in a
large refractive index change. However, to achieve a negative ∆ε the required operating
frequency is usually over 100 kHz [7]. At such a high frequency, dielectric heating [8]
becomes severe, which in turn shifts the crossover frequency toward the high frequency side.
Another technical issue of DFLC is its relatively small |∆ε| value, because a DFLC mixture
usually consists of positive ∆ε and negative ∆ε LC compounds [9]. Small |∆ε| leads to a small
Kerr constant and high operation voltage [10], which in turn causes a large hysteresis [11].
Polymer-stabilized blue phase (PSBP) [12–14], with the assist of polymer network, has
greatly expanded the BP temperature range. It is emerging as a strong contender for next-
generation display [15–18] and photonic devices [19–23]. So far, almost all the PSBPs
reported in literatures employ a positive dielectric anisotropy (∆ε>0) LC host, because it is
#172891 - $15.00 USD Received 18 Jul 2012; accepted 24 Jul 2012; published 26 Jul 2012(C) 2012 OSA 1 August 2012 / Vol. 2, No. 8 / OPTICAL MATERIALS EXPRESS 1136
easier to obtain a large, positive ∆ε LC compound than the corresponding negative one. As a
matter of fact, BPLC hosts with ∆ε>190 have been reported [24].
In this article, we report a PSBP composite with a large negative ∆ε (−11 at 1 kHz) LC
host. The polymerization extends the BP temperature range from 8 °C to 98 °C, and therefore
it enables us to study the electro-optical properties of the PSBP with a negative Kerr constant
at room temperature without noticeable dielectric heating. Due to the relatively large negative
∆ε, the measured Kerr constant is −0.16 nm/V2. Although this value is about 10X smaller than
that of a typical positive ∆ε BPLC, it is ~30X higher than that of BPLC employing a DFLC
[7]. To validate the negative sign of Kerr constant, we develop a simple measurement method
by incorporating a quarter-wave plate between the crossed polarizers. Such a polymer-
stabilized BPLC with negative Kerr constant is not only of scientific interest, it can also work
as a tunable negative C-plate for controlling the viewing angle of a LCD [25].
2. Theory
Macroscopically, the electric field-induced birefringence of a BPLC follows Kerr effect in the
low field region [26,27]:
2( ) ( ) ,ind e o
n n E n E KEλ∆ = − = (1)
where λ is the wavelength, K the Kerr constant, and E the electric field amplitude. According
to Gerber’s model [28], Kerr constant could be approximated by the following equation:
2
2,
(2 )
pK n
kελ π
≈ ∆ ∆ (2)
where ∆n is the birefringence, ∆ε the dielectric anisotropy, and k the elastic constant of the LC
host, respectively, and p is the pitch length. For a positive ∆n LC, Eq. (2) indicates that Kerr
constant is not only proportional to ∆ε, but also has the same sign. For a polymer-stabilized
BPLC with positive ∆ε, Kerr constant is positive and ne(E)>no(E), as Eq. (1) shows. But for a
negative ∆ε LC, K should be negative and ne(E)<no(E).
3. Experiment
In experiment, we fabricated a BPLC composite using a large negative ∆ε nematic LC host
SLC-10V513-200 (from SLICHEM, China). Its physical properties are listed as follows: ∆ε =
−11 at f = 1 kHz, birefringence ∆n = 0.147 at λ = 633 nm and ~22°C, and clearing temperature
Tc = 93 °C. We mixed 84.3 wt % of the host LC, 5 wt % chiral dopant R5011 (HCCH, China)
and 10.7 wt % monomers (4.7 wt % C12A and 6 wt % RM257) to form the precursor. Here,
both chiral dopant and monomers are all nonpolar so that their dielectric anisotropy is
negligible. The precursor was then filled into two cells. Cell 1 has IPS electrodes on the
bottom substrate. The ITO (indium tin oxide) electrode width and gap are both 10 µm, and
cell gap is 7.5 µm. Cell 2 is a VFS (vertical field switching) cell [29] consisting of two ITO
glass substrates (but without polyimide alignment layer) and has a cell gap of 10 µm.
Blue phase was observed from 61.9°C to 70°C during heating process and from 68.2°C to
57.8°C during cooling process. Both cells were cured at 61.2°C during cooling by a UV light
with λ~365 nm and intensity ~2 mW/cm2 for 30 min. After UV exposure, the blue phase was
stabilized with a clearing temperature Tc ~82.6°C. For benchmarking, we made another VFS
cell (Cell 3) filled with JNC JC-BP01M whose host LC has a very large positive dielectric
anisotropy (∆ε~94) [10].
4. Results and discussions
We observed Cell 1 (IPS) under a polarizing optical microscope with crossed polarizers. The
electrode direction was oriented at 45° with respect to the transmission axes of polarizers.
Figure 1 shows the microscopic textures. From Fig. 1(a), at voltage-off state (V = 0) the
#172891 - $15.00 USD Received 18 Jul 2012; accepted 24 Jul 2012; published 26 Jul 2012(C) 2012 OSA 1 August 2012 / Vol. 2, No. 8 / OPTICAL MATERIALS EXPRESS 1137
polymer-stabilized BPLC appears dark with some purple platelets, because the central
wavelength of Bragg reflection occurs at around 390 nm. Figures 1(b) and 1(c) are with a
root-mean-square voltage of 44Vrms and 60 Vrms, respectively. In the region between
electrodes, the brightness is dramatically increased, while it remains dark on the electrodes.
The increased transmittance between crossed polarizers indicates that some birefringence is
induced in the horizontal direction. As the voltage increases, transmittance gradually
increases. This phenomenon is similar to that of an IPS BPLC cell with a positive ∆ε LC host,
but it is difficult to tell whether the induced birefringence is positive or negative. We also
examined Cell 2 (VFS) under the same microscope stage and observed very similar textures at
V = 0. However, as we applied a similar voltage no noticeable brightness change was
observed. This is because the induced birefringence is along the longitudinal direction and the
incident light experiences no phase retardation and is blocked by the crossed analyzer.
Fig. 1. (a) Microscopic image of Cell 1 under crossed polarizers at V = 0, (b) at V = 44Vrms,
and (c) at V = 60Vrms; (d) Experimental setup for measuring the electro-optic properties of the
VFS cells.
To further investigate the electro-optic properties of Cell 2 (VFS), we used a similar
measurement method as reported in [29]. The setup is shown in Fig. 1(d). A He-Ne laser beam
(λ = 632.8 nm) was used as a probing light source. The VFS cell was immersed in a glass
container with glycerol (n = 1.47) so that the laser beam could enter the cell at a large angle
#172891 - $15.00 USD Received 18 Jul 2012; accepted 24 Jul 2012; published 26 Jul 2012(C) 2012 OSA 1 August 2012 / Vol. 2, No. 8 / OPTICAL MATERIALS EXPRESS 1138
due to matched refractive index. Otherwise, the incident angle would be limited by Snell’s
law. The cell was sitting on a rotary stage so that the incident angle (θ) could be controlled
easily. The transmission axes of polarizer and analyzer were set at 45° and −45° with respect
to the rotational axis of the cell, so that the ordinary (o) wave and extraordinary (e) wave
would have the same amplitude, and the phase retardation could be extracted by the measured
transmittance. A quarter-wave (QW) plate was placed after the polarizer but before the VFS
cell, with its optical axis oriented at 90° to the VFS cell’s rotational axis. Therefore, the total
phase retardation after passing the QW plate and VFS cell would be δ = π/2 + δVFS, where δVFS
= [neff(E)-no(E)]d/sinθ, and neff(E) = [(1 + tg2θ)/(1/no(E)
2 + tg
2θ/ne(E)
2)]
1/2. For a BPLC with a
positive induced birefringence (i.e., positive Kerr constant), ne(E)>neff(E)>no(E) and δVFS
increases with voltage, so the total phase δ = π/2 + δVFS increases with a starting point of π/2.
As a result, the transmittance sin2δ/2 under crossed polarizers should first increase with
applied voltage in the low field region (0<δVFS<π/2 and π/2<δ<π). On the other hand, for a
BPLC with a negative induced birefringence (i.e., negative Kerr constant), ne(E)<neff(E)<no(E)
and δVFS is a negative value, which decreases with voltage. Therefore, δ = π/2 + δVFS should
decrease as voltage increases and we should observe a decreased transmittance in the low
field region (-π/2 <δVFS<0 and 0<δ< π/2).
0 10 20 30 400.0
0.2
0.4
0.6
0.8
1.0
Tra
nsm
itta
nce
Voltage (Vrms
)
Cell 2
Cell 3
Fig. 2. Measured VT curves of Cell 2 and Cell 3 using the experimental setup in Fig. 1(d) with
a QW plate sitting in front of the VFS cells.
To validate the above analyses, we measured the voltage-dependent transmittance (VT)
curves of Cell 2 and Cell 3, and the results are plotted in Fig. 2. Here the transmittance is
normalized to that of two parallel polarizers. Since the BPLC has a relatively small negative
Kerr constant, we chose a large incident angle θ = 80° in a VFS cell in order to accumulate
sufficient phase retardation. The electric field frequency is 1 kHz. As expected, Cell 2 and
Cell 3 exhibit an opposite transmittance change in low field region, indicating their Kerr
constants are indeed with an opposite sign. The transmittance of Cell 3 (positive ∆ε) increases
with voltage until 8Vrms and then decreases as voltage further increases. This is because the
positive ∆ε BPLC in Cell 3 has a large Kerr constant, and the phase retardation δVFS reaches
π/2 (δ = π/2 + δVFS = π) at V = 8Vrms, where peak transmittance occurs. On the contrary, the
transmittance of Cell 2 (negative ∆ε) decreases as voltage increases and does not reach a
minimum due to its relatively small Kerr constant. Ideally, at V = 0 both cells should be at
50% transmittance. But as Fig. 2 shows, there is a small displacement. This phenomenon can
#172891 - $15.00 USD Received 18 Jul 2012; accepted 24 Jul 2012; published 26 Jul 2012(C) 2012 OSA 1 August 2012 / Vol. 2, No. 8 / OPTICAL MATERIALS EXPRESS 1139
be explained as follows: 1) The transmittance sin2δ/2 has the largest slope near δ = π/2,
therefore, even a small phase retardation deviation will be magnified. 2) In our VFS cell, the
incident angle is quite large (80°). A small residual birefringence from the BPLC sample or
depolarization from any optical component could lead to small phase retardation.
Next we removed the QW plate and measured the VT curve of Cell 2 again. As shown in
Fig. 3, the transmittance peak occurs at 80Vrms and the hysteresis [30] (defined as ∆V/Vp,
where ∆V is the voltage difference at half-maximum transmittance between forward and
backward, and Vp is the peak-transmittance voltage) is quite small (~1%). The dark state of
the VFS cell is not very good because of the large incident angle (80°). We used extended
Kerr model [31] to fit the VT curve, and obtained Kerr constant K = −0.16 nm/V2. The small
Kerr constant is mainly due to the relatively small dielectric anisotropy (∆ε = −11) of the host
LC.
0 20 40 60 800.0
0.2
0.4
0.6
0.8
1.0
Tra
nsm
itta
nce
Voltage (Vrms)
Forward
Backward
Fig. 3. Measured VT curve of Cell 2 using the experimental setup in Fig. 1(d) without a QW
plate in front of the VFS cell.
We also measured the response time (between dark state and peak-transmittance state) of
Cell 2 (VFS) at the room temperature. The rise time and decay time are all about 1 ms. As the
temperature increases, the response time decreases sharply, which is similar to that of positive
∆ε BPLC materials [10].
5. Conclusion
We report the results of a polymer-stabilized BPLC with a negative Kerr constant, which
originates from the negative ∆ε of the employed LC host. To experimentally prove that indeed
the BPLC has a negative induced birefringence (ne<no), we incorporated a quarter-wave plate
in our measurement system. Our material shows a negligible (~1%) hysteresis and fast
response time (~1ms) at the room temperature, although its Kerr constant is ~10X smaller
than that of a typical PSBP with a positive LC host, but this value is ~30X higher than that
using a DFLC [7]. The flattened refractive index ellipsoid can be used as a tunable C-plate for
controlling the viewing angle of a LCD.
Acknowledgments
The authors are indebted to ITRI (Taiwan) for financial support.
#172891 - $15.00 USD Received 18 Jul 2012; accepted 24 Jul 2012; published 26 Jul 2012(C) 2012 OSA 1 August 2012 / Vol. 2, No. 8 / OPTICAL MATERIALS EXPRESS 1140
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